A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. It is a polynomial of degree two in one or more variables. The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola, which may open upward or downward and varies in "width" or "steepness," but they all have the same basic "U" shape. Key features of a quadratic function include:

• Vertex: The vertex of a parabola is the point at the bottom of the "U" shape (or the top, if the parabola opens downward). The equation for a parabola can also be written in "vertex form".

• Axis of Symmetry: The axis of symmetry of a parabola is the vertical line through the vertex.

• Roots: The roots of a quadratic function are the values of x that make the function equal to zero. The quadratic formula is used to solve a quadratic equation ax^2 + bx + c = 0 and is given by x = .

Quadratic functions can be used to model a wide range of phenomena, such as the trajectory of a projectile or the profit of a business over time. They are also used extensively in calculus, where they are used to find the maximum or minimum values of functions.